Cointegration versus Spurious Regression in Heterogeneous Panels

We consider the issue of cross sectional aggregation in nonstationary, heterogeneous panels where each unit cointegrates. We first derive the asymptotic properties of the aggregate estimate, and a necessary and sufficient condition for cointegration to hold in the aggregate relationship. We also develop an estimation and testing framework to verify whether the condition is met. Secondly, we analyze the case when cointegration doesn't carry through the aggregation process, investigating whether a mild violation can still lead to an aggregate estimator that summarizes the micro relationships reasonably well. We derive the asymptotic measure of the degree of non cointegration of the aggregated estimate and we provide estimation and testing procedures. A Monte Carlo exercise evaluates the small sample properties of the estimator.